Crack Width Prediction Research Articles

Flexural Capacity and Behavior of RC Hollow Bridge Beams after a Time Service of 24 Years

The residual bearing capacity of existing bridges has been a controversial topic for engineers and technicians. In order to accurately evaluate the actual bearing capacity of a 24‐year‐old RC hollow beam bridge, its components with different thickness concrete leveling layer were removed and transported back to the laboratory. The representative static and dynamic responses of the two beams were monitored during the whole procedure. A quick assessment of loading capacity of bridge using crack height and a parameter correction method for the crack width prediction formula in the code were proposed. In addition, comparison of measured and current design codes GB 50010 and ACI 318 predicted behaviour of existing beams was also presented. The results showed that the bending process of the RC hollow beam went through the elastic phase to the elastic‐plastic phase and to the final failure. The actual flexural capacity of two beams was 10% larger than the calculated values. The natural vibration frequencies of the beam changed slightly before plastic stage, but the modal amplitude increased with the increase of degree of damage, once the beam entered plastic stage. The predicted deflections according to GB50010 were consistent with the experimental values at about 200 kN; for the code ACI, as the loading force increased, the difference between the two gradually decreased.

On a volume averaged measure of macroscopic reinforcement slip in two‐scale modeling of reinforced concrete

SUMMARYA two‐scale model for reinforced concrete, in which the large‐scale problem formulation is enriched by an effective reinforcement slip variable, is derived from the single‐scale model describing the response of plain concrete, reinforcement steel, and the bond between them. The subscale problem on the representative volume element (RVE) is correspondingly defined as finding the response of the RVE subjected to effective variables (strain, slip, and slip gradient) imposed from the large scale. A novel volumetric definition of effective reinforcement slip and its gradient is devised, and the corresponding subscale problem is formulated. The newly defined effective variables are imposed on the RVE in a weak sense using Lagrange multipliers. The response of the RVEs of different sizes was investigated by means of pull‐through tests, and the novel boundary condition type was used in FE2 analyses of a deep beam. Locally, prescribing the macroscopic reinforcement slip and its gradient in the proposed manner resulted in reduced RVE‐size dependency of effective work conjugates, which allows for more objective description of reinforcement slip in two‐scale modeling of reinforced concrete. Globally, this formulation produced more consistent amplitudes of effective slip fluctuations and more consistent maximum crack width predictions.

Predicting crack widths in FRC/reinforced concrete members using small deformation post‐crack parameters

AbstractFibers are now accepted as a means of reducing flexural and direct tension crack widths when used in combination with conventional reinforcement. However, methods used to predict in‐service crack widths incorporate performance parameters for fiber‐reinforced concrete (FRC) measured at much wider crack widths than those that occur in service. This may result in a discrepancy between tests and in‐service behavior, especially for FRC mixtures exhibiting rapidly changing performance immediately after cracking. This investigation has examined whether the crack width at which FRC performance is measured in standard beam tests has an influence on the accuracy of crack width predictions using Model Code 2010, and whether these predictions are realistic for a wide range of fiber types. The results indicate that predictions based on post‐crack residual strength appear reasonable for a wide range of fiber types, but that accuracy is improved if post‐crack performance is assessed at a crack width that more closely approximates the narrow widths that occur in service.

Modified cracked membrane model for consistent crack width predictions of reinforced concrete structures subjected to in-plane loading

The modified cracked membrane model (MCMM) presented in this paper was formulated to facilitate a mechanical calculation model that predicts crack widths in reinforced concrete (RC) structures subjected to in-plane loading for all cracking stages. It was formulated using the basic concepts of the existing cracked membrane model (CMM). Furthermore, a generalized approach for predicting the tension stiffening normal to a crack was formulated, an approach currently lacking in Eurocode 2 and fib Model Code 2010. A simplified approach for predicting the cracking behaviour of RC membranes was also proposed. Comparison with a total of 101 maximum crack widths measured experimentally on 37 test specimen from the literature showed that the MCMM provided good and consistent crack width predictions even for the cases of large rebars and covers, at which the CMM was seen to struggle. The results in this paper suggests that both the MCMM and the simplified approach show great potential for yielding reliable crack width predictions in RC membranes.

Effects of Short Fibers on the Long-Term Behavior of RC/FRC Beams Aged under Service Loading

The enhanced post-cracking properties of fiber-reinforced concrete (FRC), as compared to plain concrete (PC), are extensively proven by many experimental findings. However, still limited experimental data are available on the behavior of such materials in long-term conditions and durability. This paper shows results from a study lasting for about seven years, which was for a final discussion on the behavior in the short and long-term of steel and polyester FRC beams with conventional steel reinforcement, after being exposed to sustained service loading and natural environmental agents for 72 months. After 28 days of curing in laboratory conditions, the beams were moved to the exposure site and loaded up to service conditions. The evolution of the crack pattern was monitored and recorded over time. After this long exposure the beams were subjected to a four point bending test in order to evaluate their residual mechanical behavior. Eventually, the beams were cut, in order to carry out durability tests for the evaluation of the carbonation depth and chloride penetration. The experimental results highlight the favorable effects of short fibers in reducing crack width and enhancing flexural stiffness. The presence of short structural fibers appears also to play a useful role in delaying creep effects inside the concrete beams. Finally, the experimental cracking behavior is compared with the one computed by applying the fib Model Code 2010 for the bearing capacity and crack width prediction.

Flexural cracking behavior and crack width predictions of composite (steel + UHPC) lightweight deck system

This paper aims to clarify flexural cracking behaviors (e.g., crack width and crack spacing) of a lightweight deck system composed of steel orthotropic deck and thin ultra-high performance concrete (UHPC) layer. Forty steel-UHPC composite plates and eight steel-UHPC composite beams were tested to explore their cracking characteristics in transverse and longitudinal directions, respectively. The influences of reinforcement ratios, the thickness of the UHPC cover, the spacing of stud shear connectors, and the depth of the UHPC layers on cracking behaviors were examined. According to the bridges with composite deck systems recently constructed in China, the same spacing of reinforcing bars were employed in longitudinal and transverse directions, which ranged from 30 and 75 mm. The test results show that the occurrence and growth of cracks in UHPC layers could be effectively restricted by increasing reinforcement ratios, reducing the thickness of UHPC cover and the spacing of stud shear connectors, as well as thickening the UHPC layer. For the average crack spacing, the most significant factor was the reinforcement ratio. For the longitudinal behavior of the lightweight deck system, the steel-UHPC composite beams would fail due to the yield of steel U-ribs and the crack width in the UHPC layer would be small (e.g., 0.09–0.14 mm) when the reinforcement ratio and the thickness of UHPC cover are design appropriately. Based on the experimental observations, the formulas were developed to estimate the stress in reinforcements for the composite (steel + UHPC) lightweight deck system. The reinforcement stresses predicted by these formulas were in agreement with the experimental data. A new formulation for predicting the maximum crack width in composite (steel + UHPC) lightweight deck system was also proposed. Good agreements were achieved between the test results and the predicted values of the flexural crack width.

A Semi-Empirical Deflection-Based Method for Crack Width Prediction in Accelerated Construction of Steel Fibrous High-Performance Composite Small Box Girder.

Accelerated construction in the form of steel–concrete composite beams is among the most efficient methods to construct highway bridges. One of the main problems with this type of composite structures, which has not yet been fully clarified in the case of continuous beam, is the crack zone initiation that gradually expands through the beam width. In the current study, a semi-empirical model was proposed to predict the size of cracks in terms of small box girder deflection and intensity of load applied on the structure. To this end, a set of steel–concrete composite small box girders were constructed by the use of steel fibrous concrete and experimentally tested under different caseloads. The results were then used to create a dataset of the box girder response in terms of beam deflection and crack width. The obtained dataset was then utilized to develop a simplified formula providing the maximum width of cracks. The results showed that the cracks initiated in the hogging moment region when the load exceeded 80 kN. Additionally, it was observed that the maximum cracked zone occurred in the center of the beam due to the maximum negative moment. Moreover, the crack width of the box girder at different loading cases was compared with the test results obtained from the literature. A good agreement has been found between the proposed model and experiment results.

주파수 선택 구조를 응용한 콘크리트 구조물의 균열 폭 및 형상 예측

주파수 선택 구조를 응용한 콘크리트 구조물의 균열 폭 및 형상 예측

Crack Width and Load-Carrying Capacity of RC Elements Strengthened with FRP

The present study focuses on a prediction of crack width and load-carrying capacity of flexural reinforced concrete (RC) elements strengthened with fibre-reinforced polymer (FRP) reinforcements. Most studies on cracking phenomena of FRP-strengthened RC structures are directed to empirical corrections of crack-spacing formula given by design norms. Contrary to the design norms, a crack model presented in this paper is based on fracture mechanics of solids and is applied for direct calculation of flexural crack parameters. At the ultimate stage of crack propagation, the load-carrying capacity of the element is achieved; therefore, it is assumed that the load-carrying capacity can be estimated according to the ultimate crack depth (directly measuring concrete’s compressive zone height). An experimental program is presented to verify the accuracy of the proposed model, taking into account anchorage and initial strain effects. The proposed analytical crack model can be used for more precise predictions of flexural crack propagation and load-carrying capacity.

Experimental and theoretical investigation of crack width calculation methods for RC ties

This paper theoretically and experimentally investigates the semi‐empirical formulas recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the principles for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of nonconservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

Progress Prediction of Crack Width for Efficiency of Inspection of Centrifugal Compaction Concrete

Progress Prediction of Crack Width for Efficiency of Inspection of Centrifugal Compaction Concrete

Numerical determination of concrete crack width for corrosion-affected concrete structures

Corrosion-induced deterioration of reinforced concrete (RC) structures results in premature failure of the RC structures. In practice concrete crack width is one of the most important criteria for the assessment of the serviceability of RC structures. It is therefore desirable to predict the growth of the crack width over time so that better informed decisions can be made concerning the repairs due to concrete cracking. Literature review shows that little research has been undertaken on numerical prediction of concrete crack width. The intention of this study was to develop a numerical method to predict concrete crack width for corrosion-affected concrete structures. A cohesive crack model for concrete is implemented in the numerical formulation to simulate crack initiation and propagation in concrete. Choices for evaluating the parameters of cohesive elements are extensively discussed which is a key for developing a plausible model employing cohesive elements. The surface crack width is obtained as a function of service time. Accurate prediction of crack width can allow timely maintenance which prolongs the service life of the reinforced concrete structures.

Crack development in transverse loaded base-restrained reinforced concrete walls

The prediction and control of crack widths in reinforced concrete structures has been the subject of research for many years. However, there is still a lack of consensus on the design of reinforcement for crack control in walls with edge restraint. The paper describes an experimental programme undertaken to investigate the influence of early-age thermal contraction and long-term shrinkage on cracking in four edge-restrained reinforced concrete walls loaded in bending about their major axis. Bending was introduced as a result of initial preload as well as restraint of deflection due to volumetric change. The walls measured 3500mm long by 180mm thick with heights of 500mm and 750mm. The paper highlights the main findings of the experimental programme and presents the results of nonlinear finite element analysis that was carried out to investigate the effects of wall geometry and reinforcement ratio on crack widths in edge-restrained walls. Results suggest that crack widths in edge-restrained walls are significantly influenced by the wall geometric properties such as wall aspect ratio and wall height which are only indirectly accounted for through the restraint factor in crack width calculations to EN 1992.

Whole-process crack width prediction of reinforced concrete structures considering bonding deterioration

Monitoring the crack width of reinforced concrete (RC) structures is essential to assess their damage and durability. However, traditional methods of crack calculation are confined to the formulas for predicting the crack width in a single RC member at the service limit state. In this paper, based on the theoretical analysis of microscopic interface between concrete and rebar, an approach for the whole-process crack width prediction is proposed to trace the crack evolution of overall RC structures when subjected to cyclic loading such as earthquakes. To describe the tensile behavior characterized by the tension stiffening and tension softening effects, a modified model considering the bonding deterioration—dubbed here as the “β-ellipse model”—is formulated as an extension of conventional model based on bond-slip interaction. Then, by implementing the β-ellipse model in the framework of the fiber beam-column element model, the approach for calculating and displaying the crack width in finite element analysis (FEA) is presented. Finally, the accuracy of the developed fiber model is verified by comparing the simulated performance with extensive test results of RC members. The comparisons indicate that the model can elaborately simulate the crack width, crack distribution, crack evolution, and crack-load response of both the single cracking section and overall component, which offers a reliable and efficient tool for the whole-process crack width prediction in nonlinear FEA of RC structures.

Crack Width Prediction for Concrete Beams Strengthened with Carbon FRP Composites

AbstractStrengthening of RC beams and slabs using fiber-reinforced polymers (FRPs) is known to control crack width. However, no specific provisions are provided by most international design codes f...

A rigorous analytical model for shrinkage cracking of reinforced concrete

Concrete shrinks as it dries. If its shrinkage movement is restrained, it can crack, causing serviceability and durability problems. To ensure satisfactory performance of a reinforced concrete (RC) structure, the shrinkage crack widths are generally controlled to within acceptable limits by providing steel reinforcement for crack control. However, due to unavoidable empiricism, the design guidelines given in the various design codes for computing the amount of crack-control steel are rather inconsistent. Moreover, the various existing models for prediction of crack widths do not agree with each other, indicating that the shrinkage cracking phenomenon is still far from fully understood. With the aim of resolving this problem, a rigorous analytical model for shrinkage cracking of RC is presented. The governing equations are first derived purely based on the mechanics of the steel bar–concrete interaction. The governing equations are then solved analytically without making any unjustified assumptions. Finally, the analytical model is validated through analysis of experimental results from the literature.

Serviceability and Shear Response of RC Beams Prestressed with a Various Types of FRP Bars

The present study focuses on crack width prediction and shear response analysis of prestressed concrete (PC) beams with certain type of fiber-reinforced polymers (FRP) to be used. Recommendations are introduced taking into account the degree of bond between FRP bar and concrete interface considering a new type of FRP such as basalt FRP as well as glass FRP bars. Experimental program is presented in order to verify regulation formulae addressed for traditional steel applications. Further, a certain shear design model is proposed for PC beams consuming longitudinal basalt or carbon FRP concluding with a very accurate results.

Bond stress-slip relationship of oil palm shell lightweight concrete

This paper presents the investigation on the local bond stress-slip behaviour of lightweight oil palm shell concrete (OPSC). The bond properties of the OPSC specimen with varying reinforcing bar diameters (12 and 16mm), concrete cover sizes (50, 75 and 100mm) and compressive strengths (25 and 35MPa) were explored. A concrete cover size to reinforcing bar diameter (C/D) ratio of more than 4.17 resulted in pull-out failure while the ratio of 3.13 caused splitting cracks in the OPSC specimens. The reinforcing bar diameter, concrete cover size and compressive strength affected the normalized bond strength, provided that the splitting failure occurred in the concrete specimens. The proposed bond model for splitting failure incorporating the C/D ratio used in the closed-form solution for prediction of the serviceability crack width was found to give good estimation of the experimental results obtained from the full-scale beam tests.

Cracking behavior and crack width predictions of FRP strengthened RC members under tension

This paper presents and discusses the experimental results of uniaxial tensile tests of fiber reinforced polymer externally strengthened reinforced concrete (FRP strengthened RC) prisms in terms of crack width and crack spacing. As a non-contact and material independent system for in-time measurement of displacement and strain, the digital image correlation (DIC) technique has been used in this study for investigating the evolution of strains and formation of cracks during uniaxial tensile tests. As a result, the cracks were measured precisely at any load stage.The experimental results of tests performed by authors and other researchers on FRP strengthened RC members in tension are compared to prediction models from code provisions and guidelines (Eurocode 2 and fib 14), and their suitability are analyzed and discussed. The results show the dependence of the behavior and crack characteristics of FRP strengthened RC members to parameters such as wrapping scheme and FRP reinforcement ratios which are not included in design provisions for crack analysis. A new formulation for predicting crack width and spacing in FRP strengthened RC members, calibrated using the experimental results, has been proposed which considers all the main affecting parameters.

Flexural cracking behavior of normal strength, high strength and high strength fiber concrete beams, using Digital Image Correlation technique

The paper presents the results of an experimental work on the flexural behavior of three types of concrete: normal strength concrete (NSC), high strength concrete (HSC) and high strength fiber concrete (HSFC) in terms of crack detection, crack development, crack width measurements and strain components, using the Digital Image Correlation (DIC) technique. The experimental results of the present work and from others published in the literature were used to assess the accuracy of the major codes provisions (Eurocode 2, ACI 318 and the BS8110 code) for the crack width predictions.The comparison between the classical measurement techniques and the DIC technique suggests that both of them are suitable for the analysis of the strain components (deformations) of structural members. The most important additional benefit of the DIC technique is that it allows the easy detection of the first crack with a high precision, measures the crack opening and follows the progressive cracking process until failure of reinforced concrete members. Furthermore, the experimental results show that the addition of steel fibers increases the load at first crack and amplifies the number of cracks which leads to a remarkable decrease in both the crack spacing and crack width as well as an improvement of the ductility. The flexural failure of the beam specimens also changes from a brittle concrete crushing at the compression zone to a ductile and smooth concrete compression failure.Moreover, the present study shows that, at service load, the code’s provision on crack width are conservative for beams containing steel fibers since predicting excessively higher values than the experimental ones; the overestimation exceeded 300% in some cases and none of the present major design codes takes into consideration the positive restraining effect of the fibers on the crack widening. The Rilem technical document appears to be the only one which takes account the positive effect of steel fibers on cracking, though still not accurate enough in predicting the crack width of fiber reinforced concrete. Based on the present experimental work and on data from the literature, a modification of the Rilem mathematical model is proposed with the aim of improving the crack width prediction of this challenging concrete material.